STANDARD 10:
POLYNOMIAL OPERATIONS
Polynomial Vocabulary
Polynomial- One or more terms put together by addition and subtraction
Monomials – one term (example 4x)
Binomials- two terms (example 5x – 2)
Trinomials- three terms (example: 3x2 – 4x + 8)
Monomials – one term (example 4x)
Binomials- two terms (example 5x – 2)
Trinomials- three terms (example: 3x2 – 4x + 8)
Adding & Subtracting
Adding Polynomials
1. Combine like terms
**tip: Remember that x and x2 are not like-terms.
Example: Add (-5x + 6) and (4 – 3x)
Combine like terms -5x + – 3x and 6 + 4
-8x + 10
How to Subtract Polynomials
1. Distribute the negative 1
2. Combine like terms
Example: (9x – 4) – (-3x + 3)
9x – 4 + 3x - 3 distribute the negative
12x – 7 combine like-terms
1. Combine like terms
**tip: Remember that x and x2 are not like-terms.
Example: Add (-5x + 6) and (4 – 3x)
Combine like terms -5x + – 3x and 6 + 4
-8x + 10
How to Subtract Polynomials
1. Distribute the negative 1
2. Combine like terms
Example: (9x – 4) – (-3x + 3)
9x – 4 + 3x - 3 distribute the negative
12x – 7 combine like-terms
Multiplying Polynomials
How to:
1. Use the distributive property
2. Combine like terms
Example:
1. Use the distributive property
2. Combine like terms
Example:
Watch this great example of multiplication: http://www.virtualnerd.com/algebra-2/polynomials/trinomial-multiplication.php
Word Problems with Polynomials
Example:
The side of a cube is represented by x + 1. Find, in terms of x, the volume of the cube.
Volume = length•width•height
Volume = (x+1)(x+1)(x+1) distribute
= (x+1)(x²+2x+1) distribute
= x³+3x²+3x+1 cubic units
Watch another example here: http://www.virtualnerd.com/algebra-2/polynomials/equation-from-word-problem-solution.php
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